The present invention relates to a control apparatus for controlling a speed of an induction motor that is driven by a PWM inverter and so on. More specifically, the present invention relates to a control apparatus for controlling the speed of an induction motor at a certain value.
The speed of an induction motor (herein after sometimes referred to broadly as an "induction machine" or a "machine") is controlled by compensating a slip obtained from generated torque or from a signal proportional to the generated torque. In controlling the induction motor speed by this method, the induction motor speed changes sometimes during continuous load driving due to changes of the machine constants. Alternatively, the speed of an induction motor that does not include any speed sensor is controlled by the so-called sensor-less trans-vector control method. In controlling the speed of the induction motor by this method, the induction motor speed also changes sometimes during continuous load driving due to changes of the machine constants.
While an induction motor is continuously driving with a load, the resistance values of a stator winding and a rotor conductor rise as the temperature of the induction motor rises. Due to this, deviations occur between the machine constants set in the control apparatus and actual machine constants, and the speed of the induction motor changes.
These phenomena will be explained based on the voltage and current equations for the induction machine. The voltage equation of the induction machine that uses the d-q rotational coordinate is described by the following equation (1). Here, the d-axis is an axis of coordinate set on the magnetic flux axis of the rotating magnetic field and the q-axis is an axis of coordinate perpendicular to the d-axis. ##EQU1##
Here, r.sub.1 is a resistance value of a stator winding; r.sub.2 is a resistance value of a rotor conductor; l.sigma. is a leakage inductance; .omega..sub.1 is a primary angular frequency (applied frequency); .omega..sub.2 is a secondary angular frequency (rotating speed of the rotor); .tau..sub.2 =I.sub.m /r.sub.2 (I.sub.m is an exciting inductance); v.sub.1d is a d-axis component of a primary voltage; v.sub.1q is a q-axis component of the primary voltage; i.sub.1d is a d-axis component of a primary current (exciting current component); i.sub.1q is a q-axis component of the primary current (load current component); .PHI..sub.2d is a d-axis component of a secondary magnetic flux; .PHI..sub.2q is a q-axis component of the secondary magnetic flux; and p is a differential operator.
Assuming that the axis of the magnetic flux of the induction motor is on the d-axis in the stationary state in equation 1, .PHI..sub.2d will be constant, .PHI..sub.2q will be zero and p will be zero. By rewriting equation (1), following equations (2) through (5) are obtained. EQU .omega..sub.s1 =.omega..sub.1 -.omega..sub.2 =r.sub.2 .multidot.(i.sub.1q /.PHI..sub.2d) (2)
Here, .omega..sub.s1 is a slip angular frequency (hereinafter referred to as a "slip value"). ##EQU2##
As equation (2) indicates, the slip value .omega..sub.s1 changes as the resistance value r.sub.2 of the rotor conductor changes. As the resistance value r.sub.1 of the stator winding changes, the d-axis component of the primary current i.sub.1d changes as shown in equation (4) when v.sub.1d is constant, resulting in change of the right side of equation (3). The resulting change in the right side of equation (3) changes the denominator on the right side of equation (2), further resulting in change of the slip value .omega..sub.s1.
In short, changes of the resistance values of the stator winding and the rotor conductor cause slip value change, which further causes change of the rotating speed of the induction motor.
In view of the foregoing, it is an object of the invention to provide a control apparatus that facilitates keeping a rotating speed of an induction motor at a predetermined value by appropriately feeding the changes, caused in resistance values of a stator winding and a rotor conductor due to temperature rise in the induction motor at a time of continuous driving with a load, back to the machine constants.